This concept was "developed" in Robinson's
Mars trilogy in the sense that
themes are developed in any novel. Robinson certainly did not develop the concept in the sense of inventing it, however, as the above write up may indicate.
Indigenous cultures around present day Washington State and British Columbia, among them the Kwakiutl, Tlingit, and Chinook, had a social custom known today by its Chinook name, potlatch. Basically, rich people would throw parties and give everything they owned away, thereby garnering enormous honor.
This is one example of a gift economy, but not the only one. Gift economies typically arise in situations where the things being exchanged devalue over time, and people must put significant effort into garnering any quantity of the commodity and in so doing get more than they can personally use. Examples include: antelope shared by a hunter with their tribe, software produced by hackers and shared across the Internet, and scientific data within the scientific community. If/when nanotech ever pans out, everything will be essentially made of dirt and information, and all material possessions of any type would fall under this category.
In anthropology class I remember reading (but unfortunately could not find to preserve accuracy and give credit) a personal account of an anthropologist living on an island in the "West Indies" among an indigenous culture. The anthropologist and her husband lived in a hut and (not really understanding what it was like to live in a gift economy) assumed that it was just hypocritical exchange economy. They'd brought lots of chewing tobacco (a highly prized rarity on this island), which they "gave away" every time someone gave them a gift, such as a bunch of bananas or anthropological data. They kept giving away tobacco even when their entire front porch was covered in bananas, until someone took them aside and explained that people kept giving them bananas because it appeared that they wanted a lot of bananas; why else would they let them pile up on their porch and not give them away? The anthropologists had assumed that people would feel cheated at not getting a tobacco "gift" in exchange for their banana "gift" and entirely missed the point that you were supposed to give away anything you had too much of to whoever it seemed like needed it. It was a way of building community, it was a way of making sure people were taken care of, it really wasn't just a hypocritical exchange economy.
On a personal note, I've found that you can trick some people into participating in a gift economy of sorts. One summer I worked for a family friend, helping them clean a huge yard that had not been trimmed back for many years and had become a sort of jungle. The agreement was something along the lines of $50 a day... I didn't pay much attention to that, I just worked for a while until they asked "how many days has it been?" and I would truthfully respond "I don't know..." and they would pay me however much they thought was fair, which was generally more than I thought they strictly had to... which of course prompted me to work more diligently so they would know they weren't being "cheated" and it just sort of spiraled up until we found a comfy spot. Later I told them that I had purposefully engaged in a gift economy strategy and they just shook their head and said something about how that was too crazy to work (ignoring the fact that it actually had worked right in front of them).